2013 AMC 10B Problems/Problem 24

Problem

A positive integer $n$ is nice if there is a positive integer $m$ with exactly four positive divisors (including $1$ and $m$ ) such that the sum of the four divisors is equal to $n$ . How many numbers in the set $\{ 2010,2011,2012,\dotsc,2019 \}$ are nice?

$\textbf{(A)}\ 1 \qquad\textbf{(B)}\ 2 \qquad\textbf{(C)}\ 3 \qquad\textbf{(D)}\ 4 \qquad\textbf{(E)}\ 5$

Solution

We can check all the numbers, 2010,2011,2012, 2013,2014,2015,2016,2017,2018, and 2019 to see how many are nice. We see that 2016 is the only one, and thus the answer is (A) 1.

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2013 AMC 10B Problems/Problem 24

Problem

Solution